Aircraft: MD80
Phase of flight: Taxi
Anomaly: Flight Deck / Cabin / Aircraft Event Other / Unknown; Ground Excursion Taxiway

While [we were] taxiing for takeoff the Captain taxied off of the taxiway. [The event occurred at] an uncontrolled field; and on this particular day an event was being held which resulted in increased air and ground traffic. Both the Captain and I were monitoring our respective sides of the aircraft for traffic as we were approaching an active runway. I felt a drag on the aircraft; at which point I told the Captain to stop; as I believed that left main gear was in the grass. He said it was not; and then added power; which resulted in the aircraft sinking into the ground. He then shut down the left engine; got out of his seat; walked to the door; looked out; and verified that we were; in fact; stuck. He then returned to the cockpit; shut the aircraft down; and made the appropriate calls. We were taxing out fully loaded with freight; weighing about 90;000 LBS. We were planning...to back taxi on Runway 12 and take a left turn on the parallel taxiway north to Runway 21. This was the preferred route for us mostly due to the fact that many smaller GA aircraft were parked on the south part of the ramp (a Cessna 177 'fly-in' event was occurring that weekend and GA aircraft and traffic was much more prevalent). While making the turn at the approach end of Runway 12 I was especially concerned with looking for approaching traffic for Runway 12 or Runway 30 (since we would be taxiing down this runway). The First Officer called clear of traffic on his side (Runway 30) which I; too; could easily see and verify but I could not see the approach end of Runway 12 until I turned the aircraft. While I was conducting this turn I was looking mostly to the left and over my left shoulder; I believe that this distracted me from the quality of my turn. I either initiated the turn too soon or I inadvertently turn too sharply. As I rolled out from this turn the aircraft appeared to be; from my view; in an acceptable position on the taxiway. After taxing forward for a few more feet I felt a pulling or a sense of drag on the aircraft. I really did not believe at this time that I was in the grass. I powered up the aircraft to see if the aircraft would begin moving. It did not. At this time the aircraft was past the hold short line for Runway 12 - putting us on this active runway. The wheels were significantly entrenched in the ground. The ground was especially wet-it had been raining all night and the ground was very soft. The aircraft was positioned in such a way that there was just enough pavement under the cargo door to allow a forklift to maneuver and off load the freight. At the time of the turn the First Officer was busy getting a clearance (through a remote communication frequency) and; as it seemed to me; out of visual attention of the turn. At the time I didn't think his 'heads up' attention was necessary because it was not a low visibility situation; I was not making an extraordinary taxi maneuver; and the traffic I was concerned about would only be visible to me (looking over my left shoulder). I was upset when he told me after the fact that he knew I would hit the grass because he was noting the poor execution of this turn. This; I believe; was a lack of crucial communication between the crew. A DC9-30; departing a busy uncontrolled airport during a 'fly in' event; inadvertently exited the paved taxiway while attempting a turn to back taxi down a runway for takeoff and got bogged down in the rain softened grass. The aircraft had to be unloaded before it could be returned to the hard surface.